Question

Giraffes have excellent vision. Due to habitat, giraffes travel in small groups. Hence, they require excellent vision in order to detect predators. The eyesight of giraffes was studied in African Zoology (Oct. 2013). The researchers measured a variety of eye characteristics for 27 giraffes native to Zimbabwe, Africa. One variable measured was eye mass (in grams). The study reported xˉ= 53.4 g and s = 8.6 g.

a. Use this information to find a 99% confidence interval for the true mean eye mass of giraffes native to Zimbabwe.
b. Suppose it is known that the mean eye mass of an African water buffalo is μ=31 grams. Is it likely that the true mean eye mass of a giraffe is larger or smaller than this mean? Explain.
c. Suppose it is known that the mean eye mass of an African elephant is μ=58 grams. Is it likely that the true mean eye mass of a giraffe is larger or smaller than this mean? Explain.

Answer 1

a. The 99% confidence interval for the true mean eye mass of giraffes native to Zimbabwe is 45.4 to 61.4 grams.

b. It is likely that the true mean eye mass of a giraffe is larger than the mean eye mass of an African water buffalo.

c. It is not possible to say definitively whether the true mean eye mass of a giraffe is larger or smaller than the mean eye mass of an African elephant.

Step-by-step explanation:

a. To find a 99% confidence interval for the true mean eye mass of giraffes native to Zimbabwe, we can use the formula:

(x - z*(s/sqrt(n)), x + z*(s/sqrt(n)))

where:

• x is the sample mean (53.4 g)
• s is the sample standard deviation (8.6 g)
• n is the sample size (27)
• z is the z-score for the desired confidence level (2.576 for a 99% confidence level)

Plugging in these values, we get:

(53.4 - 2.576*(8.6/sqrt(27)), 53.4 + 2.576*(8.6/sqrt(27)))

(45.4, 61.4)

Therefore, we can be 99% confident that the true mean eye mass of giraffes native to Zimbabwe is between 45.4 and 61.4 grams.

b. Since the mean eye mass of an African water buffalo is 31 grams, and the confidence interval for the mean eye mass of giraffes native to Zimbabwe does not include 31 grams, it is likely that the true mean eye mass of a giraffe is larger than the mean eye mass of a water buffalo.

c. Similarly, since the mean eye mass of an African elephant is 58 grams, and the confidence interval for the mean eye mass of giraffes native to Zimbabwe includes 58 grams, it is not possible to say definitively whether the true mean eye mass of a giraffe is larger or smaller than the mean eye mass of an elephant.